01-21-2011 Lecture

01-21-2011 Lecture - Solu%onstotheSchrdingerEqua%on E Each...

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Solu%ons to the Schrödinger Equa%on Each wave function Ψ is a mathematical description of the shape of the standing wave corresponding to the electron An orbital E
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What is an Orbital? An orbital refers to a wavefunction, Ψ , that describes the standing wave corresponding to the electron. We will consider the lowest energy wave function Ψ 1S that corresponds to the 1S orbtial Ψ 1S
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What is an Orbital? The square of the wavefunction ( Ψ 2 ) gives the probability for finding the electron at that point in that orbital Probability = In three dimensions: Probability is spherical ( Ψ 1S ) 2 As r becomes larger, probability becomes very small, but never zero!
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What is an Orbital? 90% probability r = 2.6a 0 ( Ψ 1S ) 2 The square of the wavefunction ( Ψ 2 ) gives the probability for finding the electron at that point in that orbital Probability = ( Ψ 1S ) 2 Orbital Size
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Radial Probability 2 π r = circumference of atom Integrate 4 π r 2 = surface area of sphere at certain distance (r) Surface area is extremely small near the nucleus. a 0 = most probable radius Spherical shells, “like onion,” greatest chance (brightest, R 2 largest) near nucleus, but smaller surface area and volume (4/3) π r 3 near nucleus So radial probability, 4 π r 2 *R 2 ,ends up being greater at a finite distance away from the nucleus (not at the nucleus).
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So, what does the 1s orbital look like? Ψ
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This note was uploaded on 10/13/2011 for the course CHEM 101 taught by Professor Fitts during the Fall '08 term at UPenn.

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01-21-2011 Lecture - Solu%onstotheSchrdingerEqua%on E Each...

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